#
Concentration Quantification of TiO_{2} Nanoparticles Synthesized by Laser Ablation of a Ti Target in Water

^{*}

## Abstract

**:**

_{2}NP), which were synthesized by laser ablation of a Ti target in water. After synthesis, a colloidal solution was analyzed with UV-Vis spectroscopy. At the same time, the craters that remained on the Ti target after ablation were evaluated with an optical microscope to determine the volume of the ablated material. SEM microscopy was used to determine the TiO

_{2}NP size distribution. It was found that synthesized TiO

_{2}NP followed a Log-Normal diameter distribution with a maximum at about 64 nm. From the volume of ablated material and NP size distribution, under the assumption that most of the ablated material is consumed to form nanoparticles, a concentration of nanoparticles can be determined. The proposed method is verified by comparing the calculated concentrations to the values obtained from the Beer–Lambert law using the Mie scattering theory for the NP cross-section calculation.

## 1. Introduction

_{2}NP, as in the present work [4].

_{2}NP synthesized by the laser ablation of a Ti target immersed in water. TiO

_{2}NP have stability, corrosion resistance, low reactivity, long agglomeration, and sedimentation time. They have a broad range of industrial and scientific applications, especially photocatalysis [28]. The well-known phases of TiO

_{2}are anatase, rutile, and brookite, while amorphous TiO

_{2}, as one synthesized in this work, is much less investigated. Although amorphous TiO

_{2}is characterized by lower photocatalytic performance than one of the crystal phases, it can act as an active component for visible and near-IR light-harvesting, leading to improved photocatalytic activity in this part of the light energy spectrum, so it can also be applied in photodegradation of organic dyes, hydrogen production, and CO

_{2}photoreduction [29].

_{2}has lower toxicity and better corrosion resistance when compared to TiO

_{2}in the crystal phase, which can be an advantage in photoprotective and cosmetic applications [30]. It also exhibits excellent antibacterial properties [31], while a special energy band structure and improved charge separation may be advantageous in SERS [29]. Amorphous TiO

_{2}NP can be easily transformed to a crystalline phase by heat treatment [29], thus retaining the NP concentration value.

_{2}NP calculated from crater volume (C

_{V}) were compared to the concentrations obtained from the UV-Vis photoabsorbance data using Beer–Lambert law and Mie scattering theory (C

_{A}). Beer–Lambert law is usually used for the calculation of the concentration of metal nanoparticles with a well-defined resonant frequency, for example, gold [24,32,33] or silver as in [27]. In the case of TiO

_{2,}such calculation is more complicated because it is not plasmonic material. Still, it is a semiconductor that absorbs mainly in the UV range, so it does not possess resonant frequency. Furthermore, TiO

_{2}refractive index at some wavelength depends on many parameters such as TiO

_{2}bandgap, crystal structure, defects in it, and NP size [34,35], thus it is not easy to ensure that correct values of refraction index from literature are taken for calculation of C

_{A}. Moreover, the dipole approximation that was satisfied in [27] due to the sufficiently small size of synthesized Ag nanoparticles (<λ

_{SPR}/10, where λ

_{SPR}≈ 400 nm is silver absorption peak) is not applicable in the present work dealing with NP, which are much larger and do not possess resonant frequency. Thus, in the present paper, model verification by the Beer–Lambert law is adapted when compared to the same method used in [27] to be applicable for the determination of semiconductor NP concentration, and the Mie theory for the calculation of TiO

_{2}NP extinction cross-section is exactly applied instead of using the dipole approximation.

## 2. Materials and Methods

_{2}NP was synthesized by the pulsed-laser ablation of the Ti target (purity 99.9% and thickness 3 mm, Kurt J. Lesker) immersed in a beaker containing 40 mL of deionized water using Nd:YAG laser (Quantell, Brilliant). Laser specifications are a pulse duration of 4 ns, wavelength of 1064 nm, output energy of 290 mJ and repetition rate of 5 Hz. The laser beam was directed by a system of prisms and focused by a lens (the focal length of 10 cm) onto the target surface. The laser pulse energy in front of the target was 210 mJ while a diameter of a focused pulse on the target surface was 1 mm, which yielded a laser fluence of 27 J/cm

^{2}. The thickness of a water layer above the target was kept constant at 2 cm during the experiment to keep the ablation efficiency and thus the NP properties, constant [36]. The target was fixed during the experiments to allow the drilling of a crater and thus determine ablated material mass. A scheme of the experimental setup for PLAL is depicted in detail in [37].

_{2}NP, the produced colloid was dropped onto a silicon substrate and left to air-dry to obtain TiO

_{2}NP film. The crystalline structure of TiO

_{2}NP was investigated using a D5000 diffractometer (Siemens, Munich, Germany) in a parallel beam geometry with Cu Kα radiation, a point detector, and a collimator in front of the detector. Grazing incidence X-ray diffraction (GIXRD) scans were acquired with the constant incidence angle α

_{i}of 1°, ensuring that the information contained in the collected signal covers the entire film thickness.

_{a}) = 1.5). Results are reported as an average value of three measurements. The data processing was done by the ZS Xplorer 1.20 (Malvern Panalytical).

_{2}NP using equations from Mie scattering theory are performed by Mätzler’s MATLAB code [39].

## 3. Results

#### 3.1. TiO_{2} NP Characterization

_{2}NP. The GIXRD measurements shown in Figure 1 revealed that TiO

_{2}NP are amorphous due to the lack of appearance of any of the major Bragg peaks of TiO

_{2}phases (theoretical peaks for rutile and anatase are shown for comparison). The ζ-potential of the produced TiO

_{2}NP colloidal solution was measured to be 30 ± 1 mV, making the solution of moderate stability (aggregation and precipitation of nanoparticles appeared after two days). Therefore, TiO

_{2}NP concentration can also be considered a homogenous and well-defined value in the as-prepared solution.

_{2}NP were obtained using SEM imaging. A typical SEM image of TiO

_{2}NP is shown in Figure 2a, where 5000 pulses were applied in ablation. It can be seen that TiO

_{2}NP are spherical and with a broad range of sizes. For each number of laser pulses applied in ablation, the size distribution was obtained by measuring the diameters of 200 single nanoparticles from SEM images. It was found that the size distribution was similar for all tested numbers of pulses. The size distribution obtained from SEM images is shown in Figure 2b.

_{2}NP” is justified. Since the nanoparticles are spherical, the average NP volume ${\overline{V}}_{NP}$ is calculated as ${\overline{V}}_{NP}=\frac{1}{6}\overline{{d}^{3}}\pi $, where d is nanoparticle diameter and $\overline{{d}^{3}}$ can be obtained from the size distribution. From the given size distribution in Figure 2b, the average volume ${\overline{V}}_{NP}$ of nanoparticles is calculated as:

_{i}is the average diameter that corresponds to size range i (single column bar in size distribution), and n

_{i}= N

_{i}/N is the ratio between the number N

_{i}of nanoparticles corresponding to size range i (relative abundance of NP within corresponding column bar) and the total number of nanoparticles N. Equation (1) gives ${\overline{V}}_{NP}$ = 3.45 × 10

^{−3}μm

^{3}.

#### 3.2. Calculation of TiO_{2} NP Concentration from Crater Volume (C_{V})

_{2}NP depends on the amount of ablated material by PLAL, represented as a volume of a crater left on the target after ablation. Due to the fact that the target was made of almost pure titanium (thickness of surface oxidation layer can be neglected when compared to crater volume), the amount of titanium in the formed TiO

_{2}NP is coming solely from the target while the oxygen is coming from the water. The volume of the ablated crater V

_{crat}is turned into a fraction of titanium in the synthesized TiO

_{2}NP. The total number N of synthesized nanoparticles can be determined from the known volume of ablated material V

_{crat}by performing the following calculation:

_{2}) is the total mass of TiO

_{2}NP in colloidal solution, ρ(Ti) is Ti target density (4.506 g/cm

^{3}near R.T.), ρ(TiO

_{2}) is the TiO

_{2}NP density (3.8 ± 0.1 g/cm

^{3}) for amorphous TiO

_{2}[44], while m(Ti) and m(O

_{2}) are the total masses of titanium and oxygen atoms in TiO

_{2}NP in colloidal solution, respectively. A(O) and A(Ti) are atomic mass numbers for oxygen atom and titanium atom, which are 16 and 48, respectively. As shown in [45], TiO

_{2}NP of 21 nm in size have only 4% larger density than TiO

_{2}particles 200 nm in size, so it can be concluded that, due to the prevalence of large nanoparticles in the TiO

_{2}NP size distribution (Figure 2b), it is justified to neglect the NP size dependence of ρ(TiO

_{2}) in Equation (2).

_{V}[mL

^{−1}] of TiO

_{2}nanoparticles is then Equation (3):

_{liquid}where synthesis was performed (in our case V

_{liquid}= 40 mL).

_{crat}dependent on the number of pulses are shown, where volumes are calculated from profiles in Figure 3a, as described in [38]. For each number of applied pulses, the total number of nanoparticles in water is calculated by inserting the measured V

_{crat}in Equation (2). It provides the following number of nanoparticles dependence on number of pulses: N (1000p) = 7.69 × 10

^{9}, N (3000p) = 15.94 × 10

^{9}, N (5000p) = 20.04 × 10

^{9}. When the number of nanoparticles N is divided by water volume V

_{liquid}= 40 mL, as in Equation (3), the concentration C

_{V}of TiO

_{2}NP is obtained for each number of applied pulses. Their values are C

_{V}(1000p) = (1.9 ± 0.2) × 10

^{8}mL

^{−1}, C

_{V}(3000p) = (4.0 ± 0.4) × 10

^{8}mL

^{−1}and C

_{V}(5000p) = (5.0 ± 0.5) × 10

^{8}mL

^{−1}.

#### 3.3. Calculation of TiO_{2} NP Concentration from Beer–Lambert Law (C_{A})

_{A}of TiO

_{2}NP in colloidal solution using the Beer–Lambert law. Indirect bandgap energies for each TiO

_{2}colloidal solution are calculated from the photoabsorbance measurements using the Tauc plot as shown in the inset of Figure 4, and their values are 2.87 eV, 2.98 eV, and 3.08 eV for 1000, 3000, and 5000 laser pulses, respectively. The calculated indirect bandgap energies are close to the indirect bandgap energy 3.0 eV obtained in [46] for amorphous TiO

_{2}thin films but are also close to the bandgap energies expected for the most common TiO

_{2}phases—rutile (3.0 eV) and to a lesser extent, anatase (3.20 eV) [28].

_{A}from the Beer–Lambert law, the same size-distribution data (Figure 2b) was used for C

_{V}calculation. If ϕ

_{in}(λ) is the entrant flux, ϕ

_{out}(λ) is the output flux of light with wavelength λ through the TiO

_{2}colloidal solution, A (λ) is the absorbance at wavelength λ, defined as in Equation (4):

_{2}NP within M different size ranges, each with a concentration c

_{i}(i = 1 to M) and average optical extinction cross-section σ

_{i}(λ) within the size-range i, the absorbance A can be expressed by the Beer–Lambert law as in Equation (5):

_{2}NP. From the ζ-potential measurements, it was previously concluded that the TiO

_{2}NP colloidal solution was moderately stable. Therefore, the concentration was approximatively the same in the whole solution and can be expressed as:

_{i}is abundance (${\sum}_{i=1}^{M}}{n}_{i}=1$) of TiO

_{2}NP in the corresponding size range. Abundance n

_{i}is calculated from the size distribution (Figure 2b) for each size range. If the expression in Equation (6) for c

_{i}is inserted in Equation (5), the following expression for concentration C

_{A}is obtained:

_{2}NP at wavelength λ. σ

_{i}(λ) is approximated with extinction cross-section σ

_{ext}(d

_{i}, λ) corresponding to NP diameter d

_{i}, which is the arithmetic mean of size-range i. The Mie theory is used for the calculation of σ

_{ext}(d

_{i}, λ). According to the Mie theory, the extinction cross-section σ

_{ext}(d) of a spherical particle with diameter d is the sum of the corresponding absorption and scattering cross-section, as shown in Equation (8):

_{ext}is the extinction coefficient, which is the sum of the absorption coefficient Q

_{abs}and the scattering coefficient Q

_{scatt}.

_{ext}, Q

_{scatt}, Q

_{abs}can be calculated from Equations (9)–(11):

_{medium}is a real number, due to assumed water transparency. Wavelength-dependent values for water refraction indices used in all calculations are comprehensively listed in [48,49] for water temperature 25 °C. The Mie coefficients a

_{n}and b

_{n}can be calculated from Equations (13) and (14) [47]:

_{n}and h

_{n}are spherical Bessel’s functions of order n. m is defined in Equation (15):

_{2}refractive index, which is a complex number, defined as in Equation (16):

_{2}NP average extinction cross-section ${\overline{\sigma}}_{ext}(\lambda )={\displaystyle \sum}_{i=1}^{i=M}{n}_{i}{\sigma}_{ext}\left({d}_{i},\lambda \right)$ needed for C

_{A}calculation by Equation (7), n

_{i}values were taken from NP size distribution (Figure 2b). Equations (8)–(16) were used for the calculation of ${\sigma}_{ext}\left({d}_{i},\lambda \right)$ for each d

_{i}, with input values of wavelength and wavelength-dependent TiO

_{2}and H

_{2}O refractive indices. The refractive index of amorphous TiO

_{2}is similar to the one of anatase, and rutile to a lesser extent, as obtained in [50]. Therefore, using the values of refractive indices reported in the literature for crystallized TiO

_{2}is justified for the purpose of estimating the extinction cross-section ${\overline{\sigma}}_{ext}(\lambda )$ of the TiO

_{2}NP synthesized in this work.

_{2}refractive index on wavelength found in the each of the following works: Siefke et al. [51], Sarkar et al. [52], and Bodurov et al. [53,54], which are comprehensively listed on the website [55]. Siefke et al. [51] performed the WGP (wire grid polarizer) technique for the determination of refractive indices in ALD-prepared TiO

_{2}thin film with a thickness of 350 nm in the wavelength range of 120 nm–125 μm using TiO

_{2}material with an indirect bandgap at 3.2 eV. Sarkar et al. [52] have used opto-plasmonic sensors for the determination of the refractive indices in TiO

_{2}rutile thin film with a thickness of 200 nm in a wavelength range of 300 nm–1.69 μm. Bodurov et al. [53,54] used Bruggeman’s effective medium approximation for the calculation of refractive indices in TiO

_{2}anatase nanoparticles (diameter smaller than 35 nm) dispersed in water in the wavelength range 405–635 nm; the measurements were done with a laser micro-refractometer. The calculations of Equations (8)–(16) for the determination of ${\sigma}_{ext}\left({d}_{i},\lambda \right)$ were performed numerically, using Matzler’s MATLAB code [39].

_{2}refractive indices from all of the three mentioned works (Siefke et al. [51], Sarkar et al. [52], Bodurov et al. [53,54]) in the wavelength range 390–600 nm. From Figure 5, it can be concluded that extinction cross-sections for all three cases are very similar to each other at wavelengths 390–415 nm, corresponding to a common TiO

_{2}bandgap energy range 3.0–3.2 eV. For larger wavelengths, the difference between them is much greater. Therefore, Equation (7) will provide the best estimations of TiO

_{2}NP concentration C

_{A}while inserting A(λ) and ${\overline{\sigma}}_{ext}(\lambda )$ at wavelength λ that corresponds to bandgap energy. Furthermore, both the experimental absorbance A(λ) and Mie extinction cross-section ${\overline{\sigma}}_{ext}(\lambda )$ have larger values and therefore lower relative error at lower wavelengths, so this is another reason why C

_{A}calculation by Equation (7) has the highest accuracy at wavelengths corresponding to bandgap energy. The third advantage of such an approach is the fact that bandgap energy is easily calculated by the Tauc plot (as in Inset of Figure 4), so it is exactly known which experimental absorbances correspond to the bandgap and should be inserted in Equation (7) for the calculation of C

_{A}. These absorbances are 0.042 for 1000p, 0.072 for 3000p, and 0.090 for 5000p.

_{2}NP does not depend on the number of laser pulses. This result is expected due to the similarity in the TiO

_{2}NP size distribution at a different number of pulses. Therefore, for each number of pulses, the same average optical cross-section can be inserted in Equation (7) for C

_{A}calculation. The extinction cross-section inserted in Equation (7) for the calculation of C

_{A}is taken from calculations made by using TiO

_{2}refractive indices from Siefke et al. [51] and has a value of ${\overline{\sigma}}_{ext}$ = 5.42 × 10

^{−10}cm

^{2}at wavelength 390 nm (Figure 5), which corresponds to the bandgap of TiO

_{2}used in the same paper. The selection of the paper by Siefke et al. [51] is made due to the well-defined TiO

_{2}bandgap, which is indirect—like the TiO

_{2}NP in this paper. However, the difference in C

_{A}that would occur in the case of using TiO

_{2}refractive indices from the other two papers (Sarkar et al. [52], Bodurov et al. [53,54]) is included as the contribution to the uncertainty of C

_{A}. The calculated values of concentrations C

_{A}are: C

_{A}(1000p) = (1.8 ± 0.3) × 10

^{8}mL

^{−1}, C

_{A}(3000p) = (3.1 ± 0.5) × 10

^{8}mL

^{−1}and C

_{A}(5000p) = (3.8 ± 0.6) × 10

^{8}mL

^{−1}.

## 4. Discussion

_{V}and C

_{A}as calculated here are both listed in Table 1 and shown in Figure 7 for each number of applied pulses. C

_{A}is close to C

_{V}, but slightly lower: 5% for 1000p, 22% for 3000p, and 24% for 5000p. Therefore, our proposed method for the determination of laser-synthesized TiO

_{2}NP concentration from the size distribution and volume of the crater remained on an ablated target is verified, at least within the limits of obtained uncertainty, which are acceptable for many practical purposes.

_{A}is lower than C

_{V}. First, the actual value of the optical cross-section may be smaller than the calculated value due to the multi-scattering effects that occur on TiO

_{2}NP in colloidal solution. Second, there is a possibility that the crater volume was slightly larger than the volume of Ti material included in the formation of TiO

_{2}NP. This was due to the crater expansion that may have occurred during the Coulomb explosion in the process of laser ablation or due to the synthesis of structures that are not observable by SEM images, like Ti ions. Third, the TiO

_{2}NP analyzed in this paper are amorphous, so they probably have, according to [50], a slightly smaller refractive index than the one used for the calculation of σ

_{ext}from the paper by Siefke et al. [51]. The greatest contribution to the calculated concentration uncertainties is related to NP size-distribution uncertainty, which affects the calculation accuracy of the average volume and average optical cross-section of colloidal TiO

_{2}NP.

_{2}NP concentration using crater volumes has significant advantages over the method using Beer–Lambert law. In the calculation of concentration using the Beer–Lambert law, a complex Mie theory is applied and, therefore, numerical calculations are needed, the NP refractive indices must be known, there usually exists the upper limit of solution density for the correct absorbance determination, the high concentration homogeneity in solution is required, and in order to have more accurate results, the angular scattering in Mie theory should be considered. These issues do not exist in the method proposed in this article for the calculation of TiO

_{2}NP concentration from ablated crater volumes.

## 5. Conclusions

_{2}NP). It is based solely on the determination of the volume of an ablated material crater and the determination of the size distribution of nanoparticles. In order to verify this method, concentrations of TiO

_{2}NP in PLAL-synthesized colloidal solutions obtained by the presented method are compared to the concentrations calculated using the Beer–Lambert law. Concentrations obtained from both methods are similar: C

_{V}is 5–25% smaller than C

_{A}in the TiO

_{2}NP concentration range (1.8–5.0) × 10

^{8}mL

^{−1}. Therefore, it can be concluded that the proposed method is verified. This method has many advantages compared to traditional methods of concentration determination because it does not require a calibration solution, there is no uncertainty related to the nature of light interaction with nanoparticles, and the only requirement for NP size is the possibility of their detection by microscope. However, to apply this method correctly, the size distribution should be determined with high certainty because it is an important parameter that has a large impact on the calculated value of NP concentration, so this is the main limitation of this method. Furthermore, the method is not applicable when nanoparticles in colloidal solution are very inhomogeneous in terms of their stoichiometry or shape. It can be expected this method will also work for the calculation of the concentration of other metal oxide NP synthesized by PLAL and also while using other types of laser in PLAL, such as a pulsed femtosecond or microsecond laser, but further research may be carried out for confirmation.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**(

**a**) SEM image of TiO

_{2}nanoparticles (5000 pulses applied in ablation) and (

**b**) size distribution of TiO

_{2}NP from SEM including Log-Normal Fit.

**Figure 3.**(

**a**) Profiles of craters remained on the Ti target after ablation and (

**b**) ablation crater volume dependence on the number of pulses.

**Figure 4.**Photoabsorbance vs. wavelength measurements on TiO

_{2}colloidal solutions dependent on the number of pulses; Inset: indirect TiO

_{2}bandgap calculation from the Tauc plot for different colloidal TiO

_{2}NP solutions using the photoabsorbance data.

**Figure 5.**Extinction cross-section dependence on wavelength calculated from the Mie theory for TiO

_{2}solution of spherical nanoparticles using SEM size-distribution and TiO

_{2}refractive indices from three different works: Siefke et al. [51], Sarkar et al. [52], and Bodurov et al. [53,54] (listed on the website [55]).

**Figure 6.**The absorbance at the wavelength corresponding to the bandgap energy vs. the crater volume for TiO

_{2}colloidal solution synthesized with PLAL. Linear fit.

**Figure 7.**Dependence of TiO

_{2}concentration on a number of pulses for two different ways of concentration calculation using crater volume (C

_{V}) or the Beer–Lamber law (C

_{A}).

**Table 1.**TiO

_{2}concentrations calculated from the crater volume (C

_{V}) or from the Beer–Lambert law (C

_{A}) per number of pulses.

No. of Laser Pulses | C_{V}(10 ^{8} mL^{−1}) | C_{A}(10 ^{8} mL^{−1}) |
---|---|---|

1000 | 1.9 ± 0.2 | 1.8 ± 0.3 |

3000 | 4.0 ± 0.4 | 3.1 ± 0.5 |

5000 | 5.0 ± 0.5 | 3.8 ± 0.6 |

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**MDPI and ACS Style**

Blažeka, D.; Car, J.; Krstulović, N.
Concentration Quantification of TiO_{2} Nanoparticles Synthesized by Laser Ablation of a Ti Target in Water. *Materials* **2022**, *15*, 3146.
https://doi.org/10.3390/ma15093146

**AMA Style**

Blažeka D, Car J, Krstulović N.
Concentration Quantification of TiO_{2} Nanoparticles Synthesized by Laser Ablation of a Ti Target in Water. *Materials*. 2022; 15(9):3146.
https://doi.org/10.3390/ma15093146

**Chicago/Turabian Style**

Blažeka, Damjan, Julio Car, and Nikša Krstulović.
2022. "Concentration Quantification of TiO_{2} Nanoparticles Synthesized by Laser Ablation of a Ti Target in Water" *Materials* 15, no. 9: 3146.
https://doi.org/10.3390/ma15093146